Exercise :: Numbers  General Questions
 Numbers  Important Formulas
 Numbers  General Questions
71.  397 x 397 + 104 x 104 + 2 x 397 x 104 = ? 

Answer: Option B Explanation:

72.  (35423 + 7164 + 41720)  (317 x 89) = ? 

Answer: Option D Explanation: 35423 317 x 89 = 317 x (90 1 ) + 7164 = (317 x 90  317) + 41720 = (28530  317)  = 28213 84307  28213  56094  
73.  (x^{n}  a^{n}) is completely divisible by (x  a), when 

Answer: Option A Explanation: For every natural number n, (x^{n}  a^{n}) is completely divisible by (x  a). 
74.  Which one of the following numbers is completely divisible by 45? 

Answer: Option C Explanation: 45 = 5 x 9, where 5 and 9 are coprimes. Unit digit must be 0 or 5 and sum of digits must be divisible by 9. Among given numbers, such number is 202860. 
75.  Which of the following numbers will completely divide (3^{25} + 3^{26} + 3^{27} + 3^{28}) ? 

Answer: Option D Explanation: (3^{25} + 3^{26} + 3^{27} + 3^{28}) = 3^{25} x (1 + 3 + 3^{2} + 3^{3}) = 3^{25} x 40 = 3^{24} x 3 x 4 x 10 = (3^{24} x 4 x 30), which is divisible by30. 
76.  A number when divide by 6 leaves a remainder 3. When the square of the number is divided by 6, the remainder is: 

Answer: Option D Explanation: Let x = 6q + 3. Then, x^{2} = (6q + 3)^{2} = 36q^{2} + 36q + 9 = 6(6q^{2} + 6q + 1) + 3 Thus, when x^{2} is divided by 6, then remainder = 3. 
77.  The sum of the two numbers is 12 and their product is 35. What is the sum of the reciprocals of these numbers ? 

Answer: Option A Explanation: Let the numbers be a and b. Then, a + b = 12 and ab = 35.

78.  What will be remainder when 17^{200} is divided by 18 ? 

Answer: Option C Explanation: When n is even. (x^{n}  a^{n}) is completely divisibly by (x + a) (17^{200}  1^{200}) is completely divisible by (17 + 1), i.e., 18. (17^{200}  1) is completely divisible by 18. On dividing 17^{200} by 18, we get 1 as remainder. 
79.  If 1400 x x = 1050. Then, x = ? 

Answer: Option D Explanation:

80.  (1^{2} + 2^{2} + 3^{2} + ... + 10^{2}) = ? 

Answer: Option D Explanation:
